Homotopy over the complex numbers and generalized de Rham cohomology. (English) Zbl 0858.18008
Maruyama, Masaki (ed.), Moduli of vector bundles. Papers of the 35th Taniguchi symposium, Sanda, Japan and a symposium held in Kyoto, Japan, 1994. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 179, 229-263 (1996).
In a manner often used by A. Grothendieck, the author looks at presheaves over suitable scheme categories with values in topological spaces or such presheaves followed by the homotopy group functors. Conditions are found (the greater part of the paper) guaranteeing that such presheaves with values in topological spaces qualify as “homotopy types”. Relations with de Rham cohomology are made. The work is only at the beginning. Proofs are to be given and more interesting questions tackled.
For the entire collection see [Zbl 0842.00034].
For the entire collection see [Zbl 0842.00034].
Reviewer: P.Cherenack (Rondebosch)
MSC:
| 18F20 | Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) |
| 14F35 | Homotopy theory and fundamental groups in algebraic geometry |
| 18G60 | Other (co)homology theories (MSC2010) |
| 14F40 | de Rham cohomology and algebraic geometry |
| 14F20 | Étale and other Grothendieck topologies and (co)homologies |
| 14F05 | Sheaves, derived categories of sheaves, etc. (MSC2010) |
